Spinors for everyone

This is a document that every physicist should read before addressing the conceptual foundations of quantum mechanics. As will become clear from reading this document, using the formalism as a black box can lead to quite intricate conceptual problems. Physicists are not even aware of the insight they are missing and the transgressions of the mathematics they are making.The aim of this document is to provide the reader with all the necessary intuition he might need about the concept of a spinor to make sense of the group theory and its application to quantum mechanics. It could be used as a written basis for a series of lectures.It is hard to find intuition for spinors in the literature. We provide this intuition by explaining all the underlying ideas in a way that can be understood by everybody who knows the definition of a group, complex numbers and matrix algebra. We first work out these ideas for the representation SU(2) of the three-dimensional rotation group in R 3. In a second stage we generalize the approach to rotation groups in vector spaces R n of arbitrary dimension n > 3, endowed with an Euclidean metric. The reader can obtain this way an intuitive understanding of what a spinor is. We discuss the meaning of making linear combinations of spinors